A train runs at a speed of 90 km/h in the first 10 min, 60 km/h in the next 20 min, and 40 km/h in the last 5 minutes. What is the average speed (in km/h) of the train?
The correct answer is 65\frac{5}{7}.
The journey involved segments of travel at 90 km/h, 60 km/h, and 40 km/h for 10, 20, and 5 minutes respectively. By calculating the distance for each part and summing them, along with summing the time durations, we found the total distance to be $\frac{115}{3}$ km and the total time to be $\frac{7}{12}$ h. Dividing the total distance by the total time yields the average speed of the train as $\frac{460}{7}$ km/h or $65 \frac{5}{7}$ km/h.
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